Question

can someone please help me with a couple geometry questions

8. abcd is a parallelogram if ab=3x+4 and cd=4x-1, find the lenghth of line ab
11. in the rhombus the measure of angle 1 =168. what are the measure of angle 2 and 3
13. in quadrilateral ABCD ae=x+22 and BE=3x-18 for what value of x is ABCD a rectangle?

Answer 1

8. ab = cd
.. 3x+4 = 4x-1
.. 5 = x
.. ab = 3*5 +4
.. ab = 19


11. Adjacent vertex angles are supplementary and opposite angles are equal. If the angles are vertex angles numbered in order around the figure,
.. ∠2 = 12°
.. ∠3 = 168°


13. If the quadrilateral is a parallelogram so that point E is the midpoint of both diagonals, it will be a rectangle when the diagonals are equal length.
.. ae = be
.. x +22 = 3x -18
.. 40 = 2x
.. x = 20 . . . . . will make segments AE and BE the same length

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In general, diagrams are helpful for geometry problems.